• Journal of applied mathematics & informatics
• /
• v.41 no.1
• /
• pp.193-203
• /
• 2023

In view of solution to the Hilbert fourth problem, the present study engages to investigate the projectively flat special (𝛼, 𝛽)-metric and the generalised first approximate Matsumoto (𝛼, 𝛽)-metric, where 𝛼 is a Riemannian metric and 𝛽 is a differential one-form. Further, we concluded that 𝛼 is locally Projectively flat and have 𝛽 is parallel with respect to 𝛼 for both the metrics. Also, we obtained necessary and sufficient conditions for the aforementioned metrics to be locally projectively flat.

• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.199-203
• /
• 2000

We give nine necessary and sufficient conditions for a metric space to be complete.

• Communications of the Korean Mathematical Society
• /
• v.25 no.1
• /
• pp.59-68
• /
• 2010

In this paper, we prove common fixed point theorems for semi-compatible mappings on intuitionistic fuzzy metric space with different some conditions of Park and Kim [10]. This research extended and generalized the results of Singh and Chauhan [14].

• East Asian mathematical journal
• /
• v.18 no.2
• /
• pp.175-182
• /
• 2002

The purpose of this paper is to obtain some common fixed point theorems for multivalued mappings in fuzzy metric space. Of course this is a new result on this line.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.121-124
• /
• 2008

We will establish common fixed point theorem and example for four self maps in intuitionistic fuzzy metric space.

• East Asian mathematical journal
• /
• v.24 no.3
• /
• pp.223-232
• /
• 2008

The purpose of this paper is to prove common fixed point theorem for multivalued mappings satisfying some conditions in intuitionistic fuzzy metric space in the sense of Alaca et al.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.1
• /
• pp.157-163
• /
• 2020

Conley introduced attracting sets and repelling sets for a flow on a topological space and showed that if f is a flow on a compact metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}. In this paper we introduce chain recurrent set, trapping region, attracting set and repelling set for a flow f on a TVS-cone metric space and prove that if f is a flow on a compact TVS-cone metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.4
• /
• pp.524-529
• /
• 2008

Park et.al.[10] defined the intuitionistic fuzzy metric space in which it is a little revised in Park[4], and Park et.a1.[7] proved a fixed point theorem of Banach for the contractive mapping of a complete intuitionistic fuzzy metric space. In this paper, we will establish common fixed point theorem for four self maps in intuitionistic fuzzy metric space. These results have been used to obtain translation and generalization of Grabiec's contraction principle.

• Journal of the Architectural Institute of Korea Planning & Design
• /
• v.34 no.12
• /
• pp.49-54
• /
• 2018

Applying metric(distance) factor as weighting to spatial syntax is known to not contribute to the explanatory power for the human movement behavior as compared to the geometric(angle) factor according to the negative results of several related studies. However, Kim & Piao (2017) assumed that there is not a problem of the metric factor itself but a problem of the way of applying the metric factor as weighting, and presented a new possibility of the metric factor as weighting by proposing and verifying the methods of applying the metric weighting, which are different from the existing ones. The purpose of this study is to propose advanced methods of applying the metric weighting to space syntax, and to verify whether they contribute to the improvement of explanatory power of space syntax analysis. In this paper, we propose functions for combined depth of distance-step that combine the distance-weighted depth function with the step depth function and apply them to axial segment analysis to check the improvement of explanatory power of them.

• Korean Journal of Mathematics
• /
• v.30 no.4
• /
• pp.603-614
• /
• 2022

The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in b-metric-like spaces, which remains an extended version of corresponding results in b-metric spaces and metriclike spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in b-metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in b-metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.